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dc.creatorCastillo Santos, Francisco Eduardoes
dc.creatorDowling, Patrick N.es
dc.creatorFetter Nathansky, Helga Andreaes
dc.creatorJapón Pineda, María de los Ángeleses
dc.creatorLennard, Christopher J.es
dc.creatorSims, Braileyes
dc.creatorTurett, Barryes
dc.date.accessioned2018-11-14T07:55:08Z
dc.date.available2018-11-14T07:55:08Z
dc.date.issued2018-08-01
dc.identifier.citationCastillo Santos, F.E., Dowling, P.N., Fetter Nathansky, H.A., Japón Pineda, M.d.l.Á., Lennard, C.J., Sims, B. y Turett, B. (2018). Near-infinity concentrated norms and the fixed point property for nonexpansive maps on closed, bounded, convex sets. Journal of Functional Analysis, 275 (3), 559-576.
dc.identifier.issn0022-1236es
dc.identifier.urihttps://hdl.handle.net/11441/80137
dc.description.abstractIn this paper we define the concept of a near-infinity concentrated norm on a Banach space X with a boundedly complete Schauder basis. When k · k is such a norm, we prove that (X, k · k) has the fixed point property (FPP); that is, every nonexpansive self-mapping defined on a closed, bounded, convex subset has a fixed point. In particular, P.K. Lin’s norm in l1 [P.K. Lin, There is an equivalent norm on l1 that has the fixed point property, Nonlinear Anal. 68 (8) (2008), 2303-2308] and the norm νp(·) (with p = (pn) and limn pn = 1) introduced in [P.N. Dowling, W.B. Johnson, C.J. Lennard and B. Turett, The optimality of James’s distortion theorems, Proc. Amer. Math. Soc. 124 (1) (1997), 167-174] are examples of near-infinity concentrated norms. When νp(·) is equivalent to the l1-norm, it was an open problem as to whether (l1, νp(·)) had the FPP. We prove that the norm νp(·) always generates a nonreflexive Banach space X = R ⊕p1(R ⊕p2(R ⊕p3. . . )) satisfying the FPP, regardless of whether νp(·) is equivalent to the l1-norm. We also obtain some stability results.es
dc.description.sponsorshipConsejo Nacional de Ciencia y Tecnología (México)es
dc.description.sponsorshipMinisterio de Ciencia, Innovación y Universidadeses
dc.description.sponsorshipJunta de Andalucíaes
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherElsevieres
dc.relation.ispartofJournal of Functional Analysis, 275 (3), 559-576.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectFixed point propertyes
dc.subjectNonexpansive mappingses
dc.subjectRenorming theoryes
dc.titleNear-infinity concentrated norms and the fixed point property for nonexpansive maps on closed, bounded, convex setses
dc.typeinfo:eu-repo/semantics/articlees
dc.type.versioninfo:eu-repo/semantics/submittedVersiones
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Análisis Matemáticoes
dc.relation.projectID243722es
dc.relation.projectID613207es
dc.relation.projectIDMTM2015-65242-C2-1-Pes
dc.relation.projectIDFQM-127es
dc.relation.publisherversionhttps://reader.elsevier.com/reader/sd/pii/S0022123618301824?token=5A7CB85D9E6F6CEE1C5D39FA89AA6344E278802DEEC48061A5168A7B24250DD4BEDC2A0DB29EDF5DC3FC415D39920A4Des
dc.identifier.doi10.1016/j.jfa.2018.04.007es
dc.contributor.groupUniversidad de Sevilla. FQM127: Análisis Funcional no Lineales
idus.format.extent13 p.es
dc.journaltitleJournal of Functional Analysises
dc.publication.volumen275es
dc.publication.issue3es
dc.publication.initialPage559es
dc.publication.endPage576es

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